CCorA {vegan} | R Documentation |
Canonical correlation analysis, following Brian McArdle's unpublished graduate course notes, plus improvements to allow the calculations in the case of very sparse and collinear matrices.
CCorA(Y, X, stand.Y=FALSE, stand.X=FALSE, nperm = 0, ...) ## S3 method for class 'CCorA': biplot(x, xlabs, which = 1:2, ...)
Y |
left matrix. |
X |
right matrix. |
stand.Y |
logical; should Y be standardized? |
stand.X |
logical; should X be standardized? |
nperm |
numeric; Number of permutations to evaluate the significance of Pillai's trace |
x |
CCoaR result object |
xlabs |
Row labels. The default is to use row names, NULL
uses row numbers instead, and NA suppresses plotting row names
completely |
which |
1 plots Y reseults, and
2 plots X1 results |
... |
Other arguments passed to functions. biplot.CCorA
passes graphical arguments to biplot and
biplot.default , CCorA currently ignores extra
arguments. |
Canonical correlation analysis (Hotelling 1936) seeks linear
combinations of the variables of Y
that are maximally
correlated to linear combinations of the variables of X
. The
analysis estimates the relationships and displays them in graphs.
Algorithmic notes:
S12 %*% inv(S22) %*% t(S12) %*% inv(S11)
.
Its trace is Pillai's trace statistic.
solve
is avoided. Computation of inverses
is done by SVD (svd
) in most cases.
qr
).
The biplot
function can produce two biplots, each for the left
matrix and right matrix solutions. The function passes all arguments to
biplot.default
, and you should consult its help page for
configuring biplots.
Function CCorA
returns a list containing the following components:
Pillai |
Pillai's trace statistic = sum of canonical eigenvalues. |
EigenValues |
Canonical eigenvalues. They are the squares of the canonical correlations. |
CanCorr |
Canonical correlations. |
Mat.ranks |
Ranks of matrices Y and X1 (possibly after
controlling for X2). |
RDA.Rsquares |
Bimultivariate redundancy coefficients (R-squares) of RDAs of Y|X1 and X1|Y. |
RDA.adj.Rsq |
RDA.Rsquares adjusted for n and number of
explanatory variables. |
AA |
Scores of Y variables in Y biplot. |
BB |
Scores of X1 variables in X1 biplot. |
Cy |
Object scores in Y biplot. |
Cx |
Object scores in X1 biplot. |
Pierre Legendre, Departement de Sciences Biologiques, Universite de Montreal. Implemented in vegan with the help of Jari Oksanen.
Hotelling, H. 1936. Relations between two sets of variates. Biometrika 28: 321-377.
# Example using random numbers mat1 <- matrix(rnorm(60),20,3) mat2 <- matrix(rnorm(100),20,5) CCorA(mat1, mat2) # Example using intercountry life-cycle savings data, 50 countries data(LifeCycleSavings) pop <- LifeCycleSavings[, 2:3] oec <- LifeCycleSavings[, -(2:3)] out <- CCorA(pop, oec) out biplot(out, xlabs = NA)